On the geometry of the theory space in the ERG formalism

Abstract

We consider the theory space as a manifold whose coordinates are given by the couplings appearing in the Wilson action. We discuss how to introduce connections on this theory space. A particularly intriguing connection can be defined directly from the solution of the exact renormalization group (ERG) equation. We advocate a geometric viewpoint that lets us define straightforwardly physically relevant quantities invariant under the changes of a renormalization scheme.

23 pages

References in corpus (1)

• Exact evolution equation for the effective potential

Cited by in corpus (5)

• Essential renormalisation group
• Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety
• Recursive construction of the operator product expansion in curved space
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• The Operator Algebra at the Gaussian Fixed-Point